Algebra
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Question
Function
Evaluate the derivative
Find the domain
Find the y-intercept
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f′(x)=−14−144x5−12x
Evaluate
f(x)=9−8x−6x3×4x3−6x2−6x
Simplify
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Evaluate
9−8x−6x3×4x3−6x2−6x
Multiply
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Multiply the terms
−6x3×4x3
Multiply the terms
−24x3×x3
Multiply the terms with the same base by adding their exponents
−24x3+3
Add the numbers
−24x6
9−8x−24x6−6x2−6x
Subtract the terms
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Evaluate
−8x−6x
Collect like terms by calculating the sum or difference of their coefficients
(−8−6)x
Subtract the numbers
−14x
9−14x−24x6−6x2
f(x)=9−14x−24x6−6x2
Take the derivative of both sides
f′(x)=dxd(9−14x−24x6−6x2)
Use differentiation rule dxd(f(x)±g(x))=dxd(f(x))±dxd(g(x))
f′(x)=dxd(9)−dxd(14x)−dxd(24x6)−dxd(6x2)
Use dxd(c)=0 to find derivative
f′(x)=0−dxd(14x)−dxd(24x6)−dxd(6x2)
Calculate
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Calculate
dxd(14x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
14×dxd(x)
Use dxdxn=nxn−1 to find derivative
14×1
Any expression multiplied by 1 remains the same
14
f′(x)=0−14−dxd(24x6)−dxd(6x2)
Calculate
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Calculate
dxd(24x6)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
24×dxd(x6)
Use dxdxn=nxn−1 to find derivative
24×6x5
Multiply the terms
144x5
f′(x)=0−14−144x5−dxd(6x2)
Calculate
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Calculate
dxd(6x2)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
6×dxd(x2)
Use dxdxn=nxn−1 to find derivative
6×2x
Multiply the terms
12x
f′(x)=0−14−144x5−12x
Solution
f′(x)=−14−144x5−12x
Show Solution
Testing for symmetry
Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis
Not symmetry with respect to the origin
Evaluate
f(x)=9−8x−6x34x3−6x2−6x
Simplify the expression
f(x)=9−14x−24x6−6x2
Rewrite the function using the appropriate notation
y=9−14x−24x6−6x2
To test if the graph of y=9−14x−24x6−6x2 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=9−14(−x)−24(−x)6−6(−x)2
Simplify
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Evaluate
9−14(−x)−24(−x)6−6(−x)2
Multiply the numbers
9+14x−24(−x)6−6(−x)2
Multiply the terms
9+14x−24x6−6(−x)2
Multiply the terms
9+14x−24x6−6x2
−y=9+14x−24x6−6x2
Change the signs both sides
y=−9−14x+24x6+6x2
Solution
Not symmetry with respect to the origin
Show Solution
Graph
